Question Detail
Question
A small solid sphere with radius 0.25 cm and mass 0.56 g rolls without slipping on the inside of a large fixed hemisphere with radius 15 cm and a vertical axis of symmetry. The sphere starts at the top from rest. What is the kinetic energy at the bottom?
Correct Answer
Option D is the correct answer.
Detailed Explanation
Height difference from top to bottom of hemisphere = radius of hemisphere = 0.15 m. Potential energy lost = mgh = 0.00056 kg × 9.8 × 0.15 = 0.00056 × 1.47 = 0.0008232 J = 0.823 mJ. For rolling without slipping, KE = (7/10)mv² = mgh, so KE = 0.823 mJ ≈ 0.81 mJ.
Hint
Energy conservation: mgh = KE_trans + KE_rot.